SMU PHYS 1308  Applications of Gauss's Law and Conductors (6 pages)
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Applications of Gauss's Law and Conductors
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 6
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 Southern Methodist University
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 Phys 1308  General Physics Ii
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General Physics E M PHY 1308 Lecture Notes le home sekula Documents Notebooks PHY1308 General Physics E M PHY 1308 Lecture Notes Lecture 007 Applications of Gauss s Law and Conductors SteveSekula 8 September 2010 created 2 September 2010 no tags Goals Learn to work problems involving Gauss s Law Working with Gauss s Law As in all problems in physics all the work is in setting up the question If you can narrow down on what s being asked and how to translate that into the language of mathematics sprinkling in some physics thinking for good measure then you will be able to setup and solve hard problems I ll work two problems today to illustrate this Applying Gauss s Law A Uniformly Charged Sphere Imagine that you construct a spherical structure of charge where the charge is uniformly distributed throughout the volume whose radius is R Can you find the electric field at all points To attack this problem we can first consider the geometry We have some charge Q spread uniformly throughout this sphere That means we have a constant volume charge density Independent of the sub volume dV of the sphere we consider dq dV will be the same One can already suspect that this will come in handy for rewriting charge in termed of something we can actually integrate There are really two regions of interest in this problem points inside the sphere and points outside the sphere The distribution has spherical symmetry and so we should be able to easily use Gauss s Law to solve for the field 1 of 6 09 08 2010 10 15 AM General Physics E M PHY 1308 Lecture Notes le home sekula Documents Notebooks PHY1308 Gauss s Law works best when you have symmetry of some kind spherical planar linear Let s begin by writing down Gauss s Law Z surface dA qenclosed 0 E Let s then consider two Gaussian Surfaces a spherical surface inside the charged sphere with its own radius r r R and a spherical surface that encloses the entire charge sphere and with r R Just given the symmetry of this sphere you can already
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